Recently, practical applications of TPMSs or Tire Pressure Monitoring Systems have attracted much attention. Generally speaking, TPMSs can be classified into two categories: direct measurement and indirect measurement. In a direct measurement TPMS, the pneumatic pressure of each tire is individually measured, and in an indirect measurement TPMS, pneumatic pressure is detected from a difference in the rotation speed between two wheels. Usually, with these TPMS systems, a sensor module or unit is mounted within each tire, communicates with on-board electronics mounted with the automobile or to the body of the automobile through wireless or radio frequency (RF) transmissions.
One aspect of the TPMS is a determination of whether the tire is in rotation. Turning to FIGS. 1 through 4 of the drawings, a convention method and/or system for measuring the tire rotation is shown.
In operation (as shown in FIGS. 1 and 2), a sensor module or unit 100 is secured within a tire 102 at a predetermined location, such as the stem of tire 102. When sensor module 100 rotates together with wheel 104 and tire 102 of the automobile, in accelerator sensor or accelerometer 106 incorporated within sensor module 100, centrifugal force FC acts in the radial direction or normal direction (where center O is the axis of rotation) on accelerometer 106, while the force of gravity FG acts in the vertical direction. As a result of the rotation about center O, a corresponding normal force FN (centrifugal force FC and radial component FG sin θ of force of gravity FG) is output. Here, assuming that the mass of the movable portion of accelerometer 106 is m, the rotation speed of tire 102 is f (cycles/sec), the time is t and r is the radial distance of the sensor from the axis of rotation O, the instantaneous value of normal acceleration A is represented by following equation:
                                                                                 A                =                                ⁢                                                      F                    N                                    m                                                                                                        =                                ⁢                                                                            F                      C                                        +                                          m                      ⁢                                                                                          ⁢                      g                      ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                      θ                                                        m                                                                                                        =                                ⁢                                                                            m                      ⁢                                                                                          ⁢                                                                        r                          ⁡                                                      (                                                          2                              ⁢                              π                              ⁢                                                                                                                          ⁢                              f                                                        )                                                                          2                                                              +                                          m                      ⁢                                                                                          ⁢                      g                      ⁢                                                                                          ⁢                                              sin                        ⁡                                                  (                                                      2                            ⁢                            π                            ⁢                                                                                                                  ⁢                            ft                                                    )                                                                                                      m                                                                                                        =                                ⁢                                                                            r                      ⁡                                              (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                          f                                                )                                                              2                                    +                                      g                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                          ft                                                )                                                                                                                                                    (        1        )            If the radius of tire 102 is R and the traveling speed of the vehicle is v and rotation speed f have the relationship expressed by equation (2) below.
                    f        =                  v                      2            ⁢            π            ⁢                                                  ⁢            R                                              (        2        )            By substituting equation (2) into equation (1), one can convert to a function of speed v as shown in following formula (3).
                                                                        A                =                                                                            r                      ⁡                                              (                                                  v                          R                                                )                                                              2                                    +                                      g                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              (                                                                              v                            ⁢                                                                                                                  ⁢                            t                                                    R                                                )                                                                                                                                                                                      =                                                                                    C                        1                                            ⁢                                              v                        2                                                              +                                          g                      ⁢                                                                                          ⁢                                              sin                        ⁡                                                  (                                                                                    C                              2                                                        ⁢                            v                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                                                                    ,                                                    ⁢                                  ⁢                              where            ⁢                                                  ⁢                          C              1                                =                                                    r                                  R                  2                                            ⁢                                                          ⁢              and              ⁢                                                          ⁢                              C                2                                      =                                          1                R                            .                                                          (        3        )            
Now turning to FIG. 3, the waveform of normal acceleration A represented by equation (3) is shown. As shown, normal acceleration A varies over time with a sine waveform having a central level corresponding to centrifugal acceleration Fc/m or C1*v2 and a peak-to-peak value corresponding to acceleration due to gravity g. Waveform AM shows the waveform of normal acceleration A when running speed v is low (near zero) so that the first term of equation (3) can be ignored, and it can be approximately by the second term of equation (3).
As can be seen from FIG. 3, when the automobile starts from a stop state and the running speed rises, for the waveform of normal acceleration A with period T (1/f), central level corresponding to centrifugal acceleration Fc/m or C1*v2 rises in proportion to the square of v, which causes the peak of acceleration A to rise by the same amount. Consequently, by setting threshold Th higher than gravity acceleration g by an appropriate value h, it is possible to judge whether the automobile has substantially entered the running state by detecting whether normal acceleration A exceeds threshold Th.
However, precise and stable detection of the tire rotation at a low speed is difficult with conventional systems. As an example, assume that tire 102 has radius R of 0.35 m, rotating radius r of accelerometer 106 is 13 inches (about 0.33 m), and the automobile runs at a low speed of about 4 km/h. For normal acceleration A, the central level (C1*v2) is about 0.2-g or about 1.962 m/s2, period T (1/f) is about 1.8 s, and the waveform is a sine waveform as shown in FIG. 4. Waveform AM represented by a dot-dash line is the waveform when the automobile is at a very low speed immediately after start. In order to detect the change from waveform AM to the solid line waveform (at a speed of 4 km/h) A, one may set threshold Th close to 1.1 g or about 10.791 m/s2. In the FIG. 4, A0 through A7 represent measurement values (sample values) of normal acceleration A obtained at an interval of a predetermined time (e.g., 0.1 s) based on the output signal of accelerometer 106.
As can be seen from FIG. 4, when running at a speed of 4 km/h, measured value Ai of normal acceleration A is over threshold Th only when it is near the maximum peak value in 1 cycle (only a few rounds among the 18 sampling period), and reliable detection of rotation is difficult. Also, if a dispersion of about ±15° exists for the attachment precision of sensor module 100 or accelerometer 106, an error of about 0.04-g or about 0.392 m/s2 is generated in normal acceleration A. As a result, in this example, in order to ensure effective use of threshold Th of 1.1-g, the measurement error of accelerometer 106 must be smaller than 0.06-g or about 0.589 m/s2, and precision in absolute value is difficult to guarantee even if an expensive high performance sensor is used.
Some examples of convention systems and/or methods are: U.S. Pat. No. 5,526,263; U.S. Pat. No. 6,259,361; U.S. Patent Pre-Grant Publ. No. 2008/0030314; and PCT Publ. No. WO2005/106422.